Tactile sensation can be induced by vibration. The oscillation repeatedly stimulates nerves in the body that are sensitive to mechanical deformation. This is because acoustical waves create periodic stress-strain patterns to which nerves are sensitive. Understanding this, the greater the control the user has over this stress-strain pattern (both spatially and temporally), the more effective a stimulation device can be.
FIG. 2 illustrates a typical prior-art unbalanced-rotary-motor mechanical oscillation transducer 200, such as are commonly employed in vibrating sexual stimulation devices. Rotor 220 rotates about an axis 240 that does not pass through its center-of-mass 230. Because the center-of-mass is some distance 250 from the axis of rotation, a centrifugal force exists during rotation. The force arises from the fact that mass not under the influence of a force moves in a straight line. Because the unbalanced rotor is constrained to move in a circle, a radial force exists. This radial force is dependent on the mass of the rotor, distance from the axis of rotation 240 to the center of mass 230, and the angular velocity of the rotor 210. Using this argument, it is clear that at low angular velocity, only a small amount of energy will be transduced. Driving a harmonic oscillator with such a force makes this consequence even clearer.
Sum of forces in the x direction.
                              M          m                ⁢                                            d              2                        ⁢            x                                d            ⁢                                                  ⁢                          t              2                                          +              2        ⁢        γ        ⁢                              d            ⁢                                                  ⁢            x                                d            ⁢                                                  ⁢            t                              +                        ω          2                ⁢        x              =                  M        r            ⁢      l      ⁢                          ⁢              ω        2            ⁢              cos        ⁡                  (                      ω            ⁢                                                  ⁢            t                    )                      ⁢        
Sum of forces in the y direction
                              M          m                ⁢                                            d              2                        ⁢            y                                d            ⁢                                                  ⁢                          t              2                                          +              2        ⁢        γ        ⁢                              d            ⁢                                                  ⁢            y                                d            ⁢                                                  ⁢            t                              +                        ω          2                ⁢        y              =                  M        r            ⁢      l      ⁢                          ⁢              ω        2            ⁢              sin        ⁡                  (                      ω            ⁢                                                  ⁢            t                    )                      ⁢        
Solution to the harmonic oscillator equation in the x direction
      x    ⁡          (      t      )        =                              M          r                ⁢        l        ⁢                                  ⁢                  ω          2                                      M          m                ⁢                  Z          m                      ⁢          cos      ⁡              (                              ω            ⁢                                                  ⁢            t                    +          φ                )            
Solution to the harmonic oscillator equation in the y direction
      y    ⁡          (      t      )        =                              M          r                ⁢        l        ⁢                                  ⁢                  ω          2                                      M          m                ⁢                  Z          m                      ⁢          sin      ⁡              (                              ω            ⁢                                                  ⁢            t                    +          φ                )            
Where Zm is the mechanical impedance and ω is the natural frequency for the oscillator.
            Z      m        =                                        (                          2              ⁢              γω                        )                    2                +                              (                                          ω                2                            -                              ω                0                2                                      )                    2                                ω      0        =                  k                  M          m                    
FIG. 3 is a graph 300 showing the amplitude 310 of a prior-art unbalanced-rotary-motor oscillator driven with the frequency dependent force of the motor rotor. As the frequency 305 drops off to zero, so does the amplitude of the response of the rotary-motor oscillator. Unbalanced-rotary-motor oscillators inherently have poor low frequency performance.
Referring again to FIG. 2, the force generated by an unbalanced rotor is dependent only on the mass of the rotor, the distance from the axis of rotation to the center-of-mass 230, and the angular velocity of the rotor 220. The mass of the rotor and distance from the rotation axis are typically dependent on the physical configuration of the device, making them unchangeable during utilization. Only the angular velocity can be changed in application. Unbalanced-rotary-motor-type transducers are incapable of producing vibrations that are more complicated than sinusoids of variable frequency with amplitude that is frequency dependent as described above.
As a result of the nature of rotation, the transduced force is sinusoidal with projections in two dimensions. The two projections have a 90-degree relative phase shift. When an unbalanced-rotary-motor-type oscillator is used to couple energy into the vibrational modes of an elastic object, control over the stimulated modes is limited. Independent of orientation, at least two transverse mode orientations, or one longitudinal and one transverse mode, are stimulated. Energy cannot be coupled into a single transverse orientation. Also, only one frequency can be coupled into the medium at a time.
To improve an unbalanced-rotary-motor oscillator's low frequency performance, only one thing can be done: increase the product of the mass of the rotor and the distance it is away from the axis of rotation, both of which increase the moment of inertia of the rotor. This has two undesirable consequences: increasing the size of the device and decreasing the rate at which the oscillator can change frequencies. Another fundamental limitation exists with the unbalanced-rotary-motor-type oscillator. It is born of the fact that the amplitude of the oscillation and its frequency have a fundamental link, discussed earlier. This does not produce the necessary control required for arbitrary waveform transduction.
Many applications exist that require or could benefit from the independent control of the amplitude of the oscillation and its frequency.